When Russell writes that Hegel’s views on the philosophy of mathematics are “nonsense”, I take him to express more than mere disagreement, and something closer to an indictment of Hegel’s epistemic standards (such as standards of clarity, precision and cogency) as revealed in that area of inquiry. Furthermore, Hegel (I believe) claimed to be speaking as an expert in the field, whereas this may not be the case with the physicists speaking about the foundations of mathematics. So Russell’s conclusions about Hegel’s views in metaphysics seem to be more justified than the corresponding conclusions that the philosophers of mathematics would draw about the physicists in your example.
Hegel was a brilliant artist, though I would argue he lacked the strength of his artistic convictions. The fact that philosophy decided to imitate his artwork seems disappointing, but perhaps Plato (or Nietzsche, had he existed) should have led us to expect it.
When Russell writes that Hegel’s views on the philosophy of mathematics are “nonsense”, I take him to express more than mere disagreement, and something closer to an indictment of Hegel’s epistemic standards (such as standards of clarity, precision and cogency) as revealed in that area of inquiry. Furthermore, Hegel (I believe) claimed to be speaking as an expert in the field, whereas this may not be the case with the physicists speaking about the foundations of mathematics. So Russell’s conclusions about Hegel’s views in metaphysics seem to be more justified than the corresponding conclusions that the philosophers of mathematics would draw about the physicists in your example.
Hegel was a brilliant artist, though I would argue he lacked the strength of his artistic convictions. The fact that philosophy decided to imitate his artwork seems disappointing, but perhaps Plato (or Nietzsche, had he existed) should have led us to expect it.